A297828 Difference sequence of A297997.

1, 1, 1, 2, 2, 2, 1, 1, 2, 1, 2, 1, 3, 2, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 2, 3, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 2, 1, 1, 1, 2, 3, 2, 2, 2, 1, 1, 2, 1, 3, 2, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 3, 2, 1, 1, 3, 2, 2, 1, 1, 2, 1, 1, 1, 2, 2, 1, 2, 1

Offset

1,4

Comments

Conjectures:

(1) 2 <= a(k) <= 4 for k>=1;

(2) if d is in {1,2,3}, then a(k) = d for infinitely many k.

Links

Clark Kimberling, Table of n, a(n) for n = 1..10000

Mathematica

mex[list_, start_] := (NestWhile[# + 1 &, start, MemberQ[list, #] &]);
tbl = {}; a[0] = 1; a[1] = 2; b[0] = 3; b[1] = 4;
a[n_] := a[n] = a[1]*b[n - 1] - a[0]*b[n - 2] + n;
b[n_] := b[n] = mex[tbl = Join[{a[n], a[n - 1], b[n - 1]}, tbl], b[n - 1]];
u = Table[a[n], {n, 0, 300}](* A297826 *)
v = Table[b[n], {n, 0, 300}](* A297997 *)
Differences[u];  (* A297827 *)
Differences[v];  (* A297828 *)
(* Peter J. C. Moses, Jan 03 2017 *)

Crossrefs

Cf. A297826, A297827.

Sequence in context: A275333 A108393 A327342 * A062245 A062246 A034095

Adjacent sequences: A297825 A297826 A297827 * A297829 A297830 A297831

Keyword

nonn,easy

Author

Clark Kimberling, Feb 04 2018

Status

approved